14 of the number of geese that Farmer Gabriel had was equal to
34 of the number of geese that Farmer Luke had. When Farmer Gabriel sold 300 of his geese and Farmer Luke bought another 40, the ratio of the number of geese that Farmer Gabriel had to the number of geese Farmer Luke had become 5 : 2. What was the total number of geese that the 2 farmers had at first?
|
Make p the same (1) x 2 = (3) |
Farmer Gabriel (1) |
Farmer Luke (2) |
Make p the same (2) x 5 = (4) |
Before |
24 u |
12 u |
4 u |
20 u |
Change |
- 600 |
- 300 |
+ 40 |
+ 200 |
After |
10 p |
5 p |
2 p |
10 p |
Make the numerators the same.
1x34x3 Farmer Gabriel's geese =
3x14x1 Farmer Luke's geese
312 Farmer Gabriel's geese =
34 Farmer Luke's geese
24 u - 600 = 20 u + 200
24 u - 20 u = 200 + 600
4 u = 800
1 u = 800 ÷ 4 = 200
Total number of geese that the 2 farmers had
= 12 u + 4 u
= 16 u
= 16 x 200
= 3200
Answer(s): 3200